Numerical study on void growth in rate and temperature dependent solids

This paper is concerned about void growth and associated deformation models in porous visco-plastic solids under conditions similar to those found in highly stressed regions ahead of a crack. A plane-strain unit cell containing an initially circular void is examined to simulate the stress states during dynamic fracture of a metal. Two proportional loading rates are prescribed in the two directions of the cell and their ratio is called the "strain biaxiality" expressed in a monotonic relation with stress triaxility. Finite element analysis is performed for the effective stress-strain curves of the porous solids during void growth for a range of initial porosities, strain biaxialities, strain rates and thermal softening coefficients. Numerical results show that the void evolution and the associated non-uniform deformation depend in a complex fashion on these factors. The local zone of high stress concentration which emanates from the void spreads out in the cell to trigger non-uniform deformation and plastic yielding. Subsequently, a small zone with intense plastic strain and heating either expands smoothly near the growing voids or propagates in a specific direction determined by its interaction with the boundary conditions of the cell such as strain biaxility. At low strain biaxiality and for small voids, formation and propagation of zones with intense plastic strain and heating is localized. However, high strain biaxiality leads to rapid uniform expansion of small voids as observed experimentally. It is found that the intense heating zone follows the zone of high plastic strain concentration and diffuses with imposed strain. Thermal softening which reduces the overall stress can be neglected at the early stage of void growth, but it is magnified past the peak stress by accelerating the void growth. But in the long term, the void growth rate is insensitive to thermal softening coefficient. Increasing strain rates can promote void growth and the rate of which tends to be proportional to the eventual strain rate.